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Identifier
Values
([],1) => 0
([],2) => 0
([(0,1)],2) => 0
([],3) => 0
([(0,1),(0,2)],3) => 0
([(0,2),(2,1)],3) => 0
([(0,2),(1,2)],3) => 0
([],4) => 0
([(0,1),(0,2),(0,3)],4) => 1
([(0,2),(0,3),(3,1)],4) => 0
([(0,1),(0,2),(1,3),(2,3)],4) => 0
([(1,2),(2,3)],4) => 0
([(0,3),(3,1),(3,2)],4) => 1
([(1,3),(2,3)],4) => 0
([(0,3),(1,3),(3,2)],4) => 1
([(0,3),(1,3),(2,3)],4) => 1
([(0,3),(1,2),(1,3)],4) => 0
([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,3),(2,1),(3,2)],4) => 0
([(0,3),(1,2),(2,3)],4) => 0
([],5) => 0
([(0,1),(0,2),(0,3),(0,4)],5) => 2
([(0,2),(0,3),(0,4),(4,1)],5) => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
([(0,3),(0,4),(4,1),(4,2)],5) => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
([(0,3),(0,4),(3,2),(4,1)],5) => 0
([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 2
([(2,3),(3,4)],5) => 0
([(0,4),(4,1),(4,2),(4,3)],5) => 2
([(2,4),(3,4)],5) => 0
([(1,4),(2,4),(4,3)],5) => 1
([(0,4),(1,4),(4,2),(4,3)],5) => 2
([(0,4),(1,4),(2,4),(4,3)],5) => 2
([(0,4),(1,4),(2,4),(3,4)],5) => 2
([(0,4),(1,4),(2,3)],5) => 0
([(0,4),(1,3),(2,3),(2,4)],5) => 0
([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
([(0,4),(1,4),(2,3),(4,2)],5) => 1
([(0,4),(1,3),(2,3),(3,4)],5) => 1
([(0,4),(1,4),(2,3),(2,4)],5) => 1
([(0,4),(1,4),(2,3),(3,4)],5) => 1
([(0,4),(1,2),(1,4),(2,3)],5) => 0
([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 2
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 2
([(0,4),(1,2),(1,4),(4,3)],5) => 1
([(0,4),(1,2),(1,3),(1,4)],5) => 1
([(0,2),(0,4),(3,1),(4,3)],5) => 0
([(0,4),(1,2),(1,3),(3,4)],5) => 0
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 1
([(0,3),(0,4),(1,2),(1,4)],5) => 0
([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 3
([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2
([(0,3),(1,2),(1,4),(3,4)],5) => 0
([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 2
([(1,4),(3,2),(4,3)],5) => 0
([(0,3),(3,4),(4,1),(4,2)],5) => 1
([(1,4),(2,3),(3,4)],5) => 0
([(0,4),(1,2),(2,4),(4,3)],5) => 1
([(0,3),(1,4),(4,2)],5) => 0
([(0,4),(3,2),(4,1),(4,3)],5) => 1
([(0,4),(1,2),(2,3),(2,4)],5) => 1
([(0,4),(2,3),(3,1),(4,2)],5) => 0
([(0,3),(1,2),(2,4),(3,4)],5) => 0
([(0,4),(1,2),(2,3),(3,4)],5) => 0
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
([],6) => 0
([(3,4),(4,5)],6) => 0
([(2,3),(3,5),(5,4)],6) => 0
([(3,5),(4,5)],6) => 0
([(2,5),(3,5),(5,4)],6) => 1
([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 3
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 3
([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
([(1,5),(2,5),(3,4)],6) => 0
([(1,5),(2,4),(3,4),(3,5)],6) => 0
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 2
([(1,5),(2,5),(3,4),(5,3)],6) => 1
([(1,5),(2,4),(3,4),(4,5)],6) => 1
([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 2
([(0,5),(1,5),(2,3),(5,4)],6) => 1
([(1,5),(2,5),(3,4),(4,5)],6) => 1
([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 2
([(0,5),(1,5),(2,3),(3,4)],6) => 0
([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
([(0,5),(1,5),(2,4),(3,4)],6) => 0
([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
([(2,5),(3,4),(4,5)],6) => 0
([(1,5),(2,3),(3,5),(5,4)],6) => 1
([(1,3),(2,4),(4,5)],6) => 0
([(1,5),(3,4),(4,2),(5,3)],6) => 0
>>> Load all 116 entries. <<<
([(1,4),(2,3),(3,5),(4,5)],6) => 0
([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 1
([(0,5),(1,4),(4,2),(5,3)],6) => 0
([(1,5),(2,3),(3,4),(4,5)],6) => 0
([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 1
([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
([(0,5),(1,3),(4,2),(5,4)],6) => 0
([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
([(0,5),(1,3),(2,4),(4,5)],6) => 0
([(0,5),(1,4),(2,3),(3,4),(3,5)],6) => 1
([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 1
([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
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Description
The interval resolution global dimension of a poset.
This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
References
[1] Aoki, T., Escolar, E. G., Tada, S. Summand-injectivity of interval covers and monotonicity of interval resolution global dimensions arXiv:2308.14979
[2] https://github.com/xHoukakun/Interval-Resolution-Global-Dimension/tree/main
Created
Mar 07, 2025 at 13:26 by Jannek Müller
Updated
Mar 07, 2025 at 15:43 by Jannek Müller